Origin of size effect on efficiency of organic photovoltaics Assaf Manor, 1 Eugene A. Katz, 1,2,a) Thomas Tromholt, 3 Baruch Hirsch, 1 and Frederik C. Krebs 3 1 Department of Solar Energy and Environmental Physics, J. Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boker Campus 84990, Israel 2 The Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel 3 Risø National Laboratory for Sustainable Energy, Technical University of Denmark, Frederiksborgvej 399, DK-4000 Roskilde, Denmark (Received 13 November 2010; accepted 17 February 2011; published online 7 April 2011) It is widely accepted that efficiency of organic solar cells could be limited by their size. However, the published data on this effect are very limited and none of them includes analysis of light intensity dependence of the key cell parameters. We report such analysis for bulk heterojunction solar cells of various sizes and suggest that the origin of both the size and the light intensity effects should include underlying physical mechanisms other than conventional series resistance dissipation. In particular, we conclude that the distributed nature of the ITO resistance and its influence on the voltage dependence of photocurrent and dark current is the key to understanding size limitation of the organic photovoltaics (OPV) efficiency. Practical methods to overcome this limitation as well as the possibility of producing concentrator OPV cells operating under sunlight concentrations higher than 10 suns are discussed. V C 2011 American Institute of Physics. [doi:10.1063/1.3567930] I. INTRODUCTION Organic photovoltaics (OPV) has been suggested as an alternative to conventional photovoltaics based on inorganic semiconductor solar cells. The major advantages of OPV include their light weight, mechanical flexibility, and proc- essability (OPV cells may be solvent-processed via common low-cost, high-throughput coating and printing techniques enabling the preparation of large-area, low-cost devices). In particular, intense research is directed toward the development of OPV with a bulk heterojunction (BHJ) where donor-type conjugated polymers (hole conducting) and acceptor-type (electron conducting) fullerenes [or fuller- ene derivatives, such as [6,6]-phenyl-C61- butyric acid methyl ester (PCBM)] are mixed to form the photoactive layer. 1–3 The most studied donor/acceptor pair in the BHJ cells is poly(3-hexylthiophene) (P3HT)/PCBM. 4–7 Upon illumination, light is absorbed by the conjugated polymer resulting in the formation of a neutral and stable excited state (binding energy 0.5 eV) 8 on the polymer chain. Free carriers can be generated by exciton dissociation at a donor–acceptor interface, leaving the electron on the acceptor (fullerene in this case) and the hole on the conju- gated polymer donor. Efficient charge generation requires, therefore, that the donor and acceptor materials form inter- penetrating and continuous networks, “phase separated” on the scale of the exciton diffusion length: 10 nm. 9 Follow- ing the exciton dissociation into free carriers, the electrons and holes are conducted through the respective semiconduc- tor moieties (fullerene percolation network for electrons, and conjugated polymer chains for holes) toward the respective electrodes. Accordingly, the main difference in charge generation in organic and inorganic solar cells lies in the basic proper- ties of the photogenerated excitations. In organic solids, pho- togenerated excitations (excitons) are strongly bound and do not spontaneously dissociate into separate charges. The im- mediate consequence is that light absorption does not neces- sarily lead to the generation of free carriers and photocurrent becomes voltage dependent. 10–15 Serious progress has been achieved in the improvement of photovoltaic performance of BHJ solar cells: while the best power conversion efficiency (PCE) reported 8 years ago barely reached values higher than 1%, 3 certified efficien- cies beyond 6% and even 8% 16 are state of the art today (Table I). It is widely accepted that OPV efficiency can be limited by the cell area. All of the record efficiencies (Table I) were reported for ultrasmall BHJ OPV cells (with area 0:4 cm 2 , a low area limit for the PCE measurements sug- gested in the recent editorial report 24 ). However, no system- atic attention has been paid on the influence of the OPV cell area (size) on the key photovoltaic parameters of the devices. Experimental 25–27 and modeling 26–29 data on this effect are very limited and most of the published papers attributed the reduction of the OPV performance with increasing area to the power dissipation on the cell series resistance R s and in particular to the R s contribution by front electrode of trans- parent conductive oxide (ITO). The resistive power losses per unit area P R is given by P R ¼ R s A I 2 max ¼ R s A ðJ max AÞ 2 ¼ R s AJ 2 max ; (1) a) Author to whom correspondence should be addressed. Electronic mail: [email protected]. 0021-8979/2011/109(7)/074508/9/$30.00 V C 2011 American Institute of Physics 109, 074508-1 JOURNAL OF APPLIED PHYSICS 109, 074508 (2011) Downloaded 07 Apr 2011 to 132.72.138.1. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
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Origin of size effect on efficiency of organic photovoltaics
Assaf Manor,1 Eugene A. Katz,1,2,a) Thomas Tromholt,3 Baruch Hirsch,1
and Frederik C. Krebs3
1Department of Solar Energy and Environmental Physics, J. Blaustein Institutes for Desert Research,Ben-Gurion University of the Negev, Sede Boker Campus 84990, Israel2The Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev,Beer Sheva 84105, Israel3Risø National Laboratory for Sustainable Energy, Technical University of Denmark, Frederiksborgvej 399,DK-4000 Roskilde, Denmark
(Received 13 November 2010; accepted 17 February 2011; published online 7 April 2011)
It is widely accepted that efficiency of organic solar cells could be limited by their size. However,
the published data on this effect are very limited and none of them includes analysis of light
intensity dependence of the key cell parameters. We report such analysis for bulk heterojunction
solar cells of various sizes and suggest that the origin of both the size and the light intensity effects
should include underlying physical mechanisms other than conventional series resistance
dissipation. In particular, we conclude that the distributed nature of the ITO resistance and its
influence on the voltage dependence of photocurrent and dark current is the key to understanding
size limitation of the organic photovoltaics (OPV) efficiency. Practical methods to overcome this
limitation as well as the possibility of producing concentrator OPV cells operating under sunlight
concentrations higher than 10 suns are discussed. VC 2011 American Institute of Physics.
[doi:10.1063/1.3567930]
I. INTRODUCTION
Organic photovoltaics (OPV) has been suggested as an
alternative to conventional photovoltaics based on inorganic
semiconductor solar cells. The major advantages of OPV
include their light weight, mechanical flexibility, and proc-
essability (OPV cells may be solvent-processed via common
low-cost, high-throughput coating and printing techniques
enabling the preparation of large-area, low-cost devices).
In particular, intense research is directed toward the
development of OPV with a bulk heterojunction (BHJ)
where donor-type conjugated polymers (hole conducting)
and acceptor-type (electron conducting) fullerenes [or fuller-
ene derivatives, such as [6,6]-phenyl-C61- butyric acid
methyl ester (PCBM)] are mixed to form the photoactive
layer.1–3 The most studied donor/acceptor pair in the BHJ
cells is poly(3-hexylthiophene) (P3HT)/PCBM.4–7
Upon illumination, light is absorbed by the conjugated
polymer resulting in the formation of a neutral and stable
excited state (binding energy �0.5 eV)8 on the polymer
chain. Free carriers can be generated by exciton dissociation
at a donor–acceptor interface, leaving the electron on the
acceptor (fullerene in this case) and the hole on the conju-
and for dominant space charge limitation a¼ 0.75].11,12
The values G and a are extracted by:
lnðJscÞ ¼ lnðGÞ þ alnðPinÞ: (4)
By this purpose we replotted the data shown in Fig. 3(a) in a
log–log scale and then subdivided every curve by two parts:
linear (a1 is very close to 1) and sublinear (a2 < 1) (with the
curve-fitting coefficient of determination R2 higher than 0.99
for all extracted parameters).
Table II shows the results of such analysis
One can see that:
(1) G1 and G2 values are higher for smaller cells, implying
better current extraction (even in the linear regime);
(2) For smaller cells, the linear regime extends further to-
ward higher concentrations (see the column “a1:a2 bor-der” with the approximate concentration levels (in suns)
where the data starts to deviate from linearity).
B. Light intensity dependence of VOC
For a p–n junction solar cell:
VOC ¼ ðnkT=qÞ½lnðJph=J0 þ 1�; (5)
Jph ¼ Jlight � Jdark; (6)
where n is a p–n junction quality factor (for an ideal p–njunction cell, n¼ 1), Jph is photocurrent density, Jlight and
Jdark are the cell current densities measured under illumina-
tion and in the dark, respectively [see Fig. 4(a)].
Since in inorganic PV the voltage-independent Jph is
approximately equal to JSC and linearly proportional to c:
VOC � ðnkT=qÞlnðJSC=J0Þ¼ðnkT=qÞlnðcÞ þ const: (7)
Figure 5(a) shows light intensity dependence of VOC [shown
in Fig. 3(b)] replotted in the scale “VOC vs ln (JSC)” in order
to extract n values according to Eq. (7). One can see that the
data can be linearly fitted and the slopes of the linear fits and
the corresponding n values decrease with the cell size
decrease. Values of n are summarized in Table II. However,
TABLE II. Analysis of the light intensity dependence of JSC and comparison of diode quality factors n obtained by three different methods: fitting the curves
VOC vs ln(JSC); fitting the curves VOC vs ln(Jph@VOC); fitting the dark J–V curves.
Cell area (cm2) G1 a1 Ga a2 a1:a2 border (suns) n (JSC) n (Jph@VOC) n (Jdark)
1 5.03 0.99 5.33 0.66 4.5 1.5 4.7 4.5
0.25 6.36 1 5.75 0.86 6.53 1.3 3.1 2.5
0.04 6.77 1 9.4 0.82 19.44 1.2 2.4 1.8
aReference 38.
FIG. 4. (Color online) (a) J–V curves of
the 1 cm2 cell measured in the dark and
under illumination of 1 sun. It is evident
that the Jph¼ Jlight� Jdark measured at
the short-circuit conditions (Jph � JSC)
is much higher that that measured at
open circuit (VOC¼ 0.59 V). Compensa-
tion voltage V0 at which Jlight¼ Jdark is
also indicated (V0¼ 0.64 V). (b) The
same curves replotted as Jph vs Veff ¼V0
– V. Veff values for open-circuit (OC)
and short-circuit (SC) conditions are
indicated.
074508-4 Katz et al. J. Appl. Phys. 109, 074508 (2011)
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these n values contradict with those obtained by the treat-
ment of the dark J–V curves of the same cells (Fig. 2).
Forward-biased dark J–V curves are represented by
three successive regimes:40 local leakage current, injection
current (J ! exp[qV/nkT]) and space charge limited current
(J ! V0.5/d3). Thus the semilogarithmic plots of the dark
J–V curves (Fig. 2) in the injection current regime
(0.5 V<V< 0.7 V, marked by an arrow in Fig. 2) has a
slope of q/nkT. The obtained n values are shown in Table II.
One can see that they are considerably higher than those
obtained with Eq. (6) and Fig. 5(a).
This contradiction is due to the above-mentioned fact
that, because of the excitonic nature of photogeneration in
OPV, the photocurrent itself is voltage-dependent.10–15 It is
clearly seen in Fig. 4(a) and will be discussed in detail in the
following (Sec. III C). Accordingly, in order to get more
accurate n values we suggest using a semilogarithmic plot of
VOC and Jph¼ Jlight� Jdark measured at open-circuit condi-
tions, Jph@VOC) [Fig. 5(b), Table II]. This limits our range
of interest to the VOC voltage range, and therefore to the cor-
responding Jph range—which equals exactly (�Jdark). One
can see the better agreement of these data with those
obtained by the treatment of the dark J�V curves, as again,
smaller cells are characterized by lower n values.
Although a microscopic model for n in BHJ OPV is
missing, it is accepted that the ideality factor reflects the
“opening behavior” of the diode with the applied voltage
with respect to its recombination behavior.41 It was also pro-
posed for OPV that n> 2 could be related to the tunneling
effect42 (where recombination is intensified by tunneling of
charge carriers) or due to reduced mobility in disordered
materials where Einstein relation is generalized and can dif-
fer from its classical form with n¼ 1.43 Anyway, a change in
the ideality factor could be evidence of a different type of
mechanism for the recombination losses at the junctions.
C. Light intensity dependence FF: Evolution of theshape Jph–V curves with illumination
Let us discuss now the field (voltage) dependence of Jph
as a possible underlying mechanism for the shape deteriora-
tion of the J–V curves and, as a result, for the light intensity
dependence of FF.
Photogeneration of free charge carriers in OPV is pre-
ceded by the dissociation of excitons at the donor–acceptor
interface. The formation of free electron and hole pairs is a
highly field-dependent process, which is reflected in the
strong voltage dependence of Jph. To study this dependence
it is widely accepted10–15 to plot Jph¼ Jlight – Jdark against
the effective applied bias voltage (V0 – V), where V0 is the
compensation voltage, defined by the voltage at which the
Jph¼ 0, i.e., Jlight¼ Jdark [see Fig. 4(b)].
For example in short circuit (SC), V¼ 0 and the built-in-
potential at the junction Veff ¼V0 [regime of strong field,
V0¼ 0.64 V in Fig. 4(b)]. In open-circuit (OC), Veff
¼V0�VOC [0.05 V in Fig. 4(b)]. In this regime the built-in-
voltage is low and the field across the junction is weak.
Strong voltage dependence of Jph reduces the FF signifi-
cantly.44 From the shape of the Jph curve it is possible to
characterize the carrier photogeneration and transport in dif-
ferent regimes. Indeed, the behavior of the illuminated J–Vresponse depends on the drift length (LD¼ msE, where m is
the mobility, s is the lifetime of the charge carriers, and E is
the field across the device) of the electrons (e) and holes (h)
and the ratio (b) of their drift lengths (b¼mese/mhsh). For bal-
anced transport (b � 1), Jph varies linearly with Veff at lower
voltage regime and at higher voltage (Vsat) it saturates to a
value Jph¼ qGL, where G is the generation rate, and L is the
thickness of the active layer.
Saturation of Jph happens when all generated carriers are
extracted. If Vsat>V0 [SC at Fig. 4(b)], the charge collection
efficiency does not approach 100% even under short-circuit
conditions. As Vsat moves closer to OC it results in the
increasing FF and vice versa.
In case of unbalanced transport (b< 1 or b> 1), which
is also known as ‘‘ms-limited” process, carrier accumulation
takes place near both contacts, modifying the field. In an
extreme case (b� 1 or b� 1), the slower charge carrier
will accumulate near one of the electrodes to a greater
extent, leading to buildup of an internal field. When the field
in this region becomes equal to the external applied voltage
V, the current becomes ‘‘space charge limited” (SCL). Jph !V0.5 in both SCL and ms-limited cases. However, the Jph
varies linearly with G, hence with the intensity of illumina-
tion (Pin or c) in ms-limited case and shows a three-quarter
dependence on G in the SCL case. The square root depend-
ence on voltage limits the maximum possible FF to 42% in
the SCL case.11
Figure 6 shows the voltage dependence of Jph in a dou-
ble logarithmic scale for three cells of different areas and
three levels of illumination (�1,�5, and �10 suns).
FIG. 5. (Color online) VOC as a function
of Ln (JSC) (a) and Ln (Jph@VOC) (b).
074508-5 Katz et al. J. Appl. Phys. 109, 074508 (2011)
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One can see from Fig. 6(a) that the photocurrent is
approximately equal for the three sizes at �1 sun. The satu-
ration values differ a little but the field dependence is similar,
meaning that, at this level of illumination, there is no size
effect on the photocurrent. The reduced FF value for the
larger cell [Fig. 3(c)] should be controlled by a different
mechanism (effect of the dark current for example, see the
following).
For higher levels of illumination [Figs. 6(b) and 6(c)]
the size effect on the photocurrent is evident: the smallest
cell reaches saturation regime at lower Veff than the larger
one and the saturation value itself is higher. Such behavior
controls both FF (via the location of the MPP on the Jph
curve, as will be discussed in Sec. III C) and JSC and can
explain the size effect on these parameters at high
concentrations.
One can see however, that for all concentrations, all the
cells behave linearly in the low field regime (there is no evi-
dence of SCL effect).
Figure 7 shows the irradiance dependence of Jph for the
cells of various sizes at SC, MPP, and OC conditions.
One can observe that as Veff decreases (going from SC
to OC) the nonlinear behavior starts to be exhibited. The first
that enters the nonlinear regime is the largest cell—see
behavior for SC and MPP [Figs. 7(a) and 7(b)] while at OC
all three cells behave nonlinearly at all concentrations
[Fig. 7(c)].
Data shown in Fig. 7(a) are in accordance with the results
for JSC [Fig. 3(a)]: for high illumination levels the smaller cell
is still in the linear regime of JSC–C, while the larger cells
suffer from sublinear behavior.
Thus, we can conclude that the voltage-dependent pho-
tocurrent behavior can be responsible for the size effect on
FIG. 6. (Color online) Dependence of Jph on Veff ¼V0 – V in a log–log scale
for three representative cells with various areas measured under �1 sun (a),
�5 suns (b), and �10 suns (c). The line marks the slope of 1 for comparison
(Jph ! Veff). Positions of OC, maximum power point (MPP), and SC are
indicated by diamonds, circles, and stars, respectively.
FIG. 7. (Color online) Light intensity dependence of Jph for the cells of vari-
ous sizes at SC (a), MPP (b), and OC (c).
074508-6 Katz et al. J. Appl. Phys. 109, 074508 (2011)
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both JSC and FF (at least for C> 1). However, two questions
still remain open:
(1) Why is the voltage dependence of Jph stronger for larger
cells?
(2) What controls the effect at low illumination levels
(C� 1)?
To try and answer the second question let us discuss
what controls FF at low light intensities.
Figure S4a in supplementary material38 demonstrates
voltage dependence for all three currents (Jdark, Jlight and
Jph¼ Jlight - Jdark) measured at 1 sun. Although Jph for all
three cells are similar, the Jlight curves exhibit differences
(that result in the lower FF for the larger area) and this differ-
ence is due to the corresponding difference in the Jdark
curves.
However, for C> 1 (the case of 5 and 10 suns are shown
in Figs. S4b-c supplementary material38) it is evident that the
Jlight curves (i.e. JSC, FF, and the corresponding size effects)
are completely controlled by Jph behavior.
D. On the underlying mechanism of the size effect inOPV cells
The observed results can be explained on the basis of a
model presenting a distributed series resistance of the ITO
front electrode in OPV (Refs. 26 and 45) or any other similar
electrodes in which current flows parallel to the cell surface
(Fig. 8).
The current density J is not constant along the device
because the charges that flow from the side distant to the
extracting contact experience more series resistance. Simula-
tions (see Fig. 4 in Ref. 44) show that there is a reduction in
current density and increase in voltage across the active layer
along the dimension x in Fig. 8.
For each voltage applied to the cell (Va) there is a volt-
age drop along the distance from the current-extracting con-
tact (marked by a dash in Fig. 8). This drop causes the
increase in voltage across the junction (Vjn) and the reduction
in the current from the distant parts of the cell, caused by the
diodes’ opening when Vjn increases45 and by the voltage de-
pendence of Jph (Fig. 6). In other words, even if Va¼ 0, not
all parts of the cell are under SC conditions. Unfortunately,
the authors of Ref. 45, assumed in their simulations that pho-
tocurrent is voltage independent (Jph¼ const). Therefore,
they only demonstrated a partial effect on FF (current
at Va> 0) but did not observe any effect on JSC (constant
current for Va¼ 0 in Fig. 5 in Ref. 45). The effect of cell size
on FF via the distributive series resistance is well known for
inorganic solar cells. However, in OPV it also influences the
voltage-dependent Jph (Figs. 6 and 7). This influence can
explain the JSC behavior [Fig. 3(a)] and provide an additional
mechanism for FF degradation. Indeed, if the maximum
power point is situated considerably below the saturation re-
gime in the Jph–Veff curve [as demonstrated in Figs. 6(b) and
6(c)], voltage difference along the cell’s active layer (due to
the ITO distributive resistance) causes a large decrease in Jph
in the cell areas that are far from the current extracting con-
tact, and, as a result, strong decrease in FF.
The discussed mechanism is dependent on the dimen-
sion of the cell (the distance x from the contact). Anyway,
the effect should increase for large area cells while the
smaller area cells should exhibit better performance.
The phenomenon is fundamental and should take place
in any OPV or other excitonic (with voltage-dependent
photocurrent) solar cells15 with ITO front electrode or any
other similar transparent electrodes (graphene46,47 and car-
bon nanotube electrodes,48 surface-plasmon enhanced Ag
grids,49 metal nanowire mesh,50 etc.) in which current flows
parallel to the cell surface. The effect intensifies with illumi-
nation level. The illumination level at which the effect starts
to be a dominant limiting factor for a certain solar cell may
depend on the cell area, resistivity of the transparent elec-
trode, electronic properties of the active layer, etc. We sug-
gest also that this effect can be significant even in the case
when the ITO electrode contribution to the Rs dissipation of
the entire cell is not dominant. However, practical methods
to overcome such size limitation and produce efficient large-
area OPV cells and modules can be similar to those for
reduction of ITO distributive resistance, for example deposi-
tion of metal subgrid on the ITO layer.27,51 Our results also
suggest that by using this technological approach one can
produce future concentrator OPV cells operating under sun-
light concentrations higher than 10 suns. The latter of course
will raise new challenges for OPV stability at these illumina-
tion levels.35
It is important to add here, that the suggested loss-mech-
anism analysis also can be relevant in a situation where Jph is
considered to be voltage-independent while recombination
losses are charge-density dependent.52 Whether the
FIG. 8. (Color online) Simplified one-dimensional
graphic sketch for a solar cell with distributive series
resistance.
074508-7 Katz et al. J. Appl. Phys. 109, 074508 (2011)
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additional loss is originated from voltage dependence of pho-
togeneration or enhanced bimolecular recombination, it
should depend on the voltage drop along the device front
electrode.
Finally, we suggest that the cell’s dark current is also
affected by the same mechanism. At forward bias the charge
carriers are injected into the device and are recombined in
the active layer. When the voltage across the ITO layer is
not equal, the most distant locations will experience reduced
fields and therefore reduced forward currents, thus lowering
the quality of the entire diode. It is manifested in the deterio-
ration of the dark J–V curve shape and the effect intensifies
with the cell area (as shown in Fig. 2, Table II). Our sugges-
tion is supported by the experimental results on the reduction
of electroluminescence intensity with increasing area of ITO
transparent electrodes in organic LEDs.53
We therefore conclude that the effect of distributed re-
sistance of the transparent electrode can limit the cell FF in
high and low illumination regimes in two ways: (1) by the
decrease of the photocurrent via its dependence on the
applied voltage (high C); and (2) by the decrease of the diode
quality factor and the corresponding deterioration of the dark
J–V curve (mainly in lower C regime).
V. CONCLUSIONS
1. The I–V curves of as-produced OPV cells of various areas
(1, 0.25, and 0.04 cm2) were measured under different
sunlight concentrations (from 0.2 to 100 suns) and light
intensity dependence of the OPV key parameters (ISC,
VOC, FF, PCE) was analyzed.
2. We demonstrated experimentally that increase in the cell
area results in:
(a) decrease in the short-circuit current density (this is
true for all sunlight concentrations but the effect
amplifies with the concentration increase);
(b) decrease in FF for all light intensities (low and high
concentration regimes);
(c) decrease of the PCE values for all light intensities
(low and high concentration regimes) and shift (to
higher illumination) of the peak PCE light intensity;
(d) increase of the diode quality factor n3. All the results can be consistently explained by the volt-
age dependence of photocurrent Jph (incomplete exciton
separation) and the dark current in the presence of signifi-
cant distributed series resistance of the ITO front elec-
trode or any other similar transparent electrodes in which
current flow parallel to the cell surface.
4. The discussed phenomenon is fundamental and should
take place in any OPV or other excitonic (with voltage-
dependent photocurrent) solar cells with highly resistive
transparent electrode. The effect intensifies with the illu-
mination level. The light intensity at which the effect
starts to be significant for certain solar cells may depend
on the cell area, resistivity of the electrodes, electronic
properties of the active layer, etc.
5. The results are important for both a basic understanding
of the operation of excitonic solar cells and for the practi-
cal purpose of producing efficient large-area OPV cells
and modules. The possibility of producing concentrator
OPV cells operating under sunlight concentrations is
higher than 10 suns and is discussed.
ACKNOWLEDGMENTS
This work was performed, in part, in the framework of
the “Largecells” project that received funding from the Euro-
2007-2013) under Grant Agreement No. 261936.” T.T. and
F.C.K. thank the Danish Strategic Research Council (2104-
07-0022) and EUDP (j. nr. 64009-0050) for financial sup-
port. E.A.K. acknowledges financial support by the FIRST -
Focal Initiatives in Science and Technology foundation of
the Israel Science Foundation (grant no. 1004/07).
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